Solve 3a^2/a-4-a+2/2a-8*96/a^2+2a

$$\frac { 3 a ^ { 2 } } { a - 4 } - \frac { a + 2 } { 2 a - 8 } \cdot \frac { 96 } { a ^ { 2 } + 2 a }$$

Evaluate

$$\frac{3\left(a^{3}-16\right)}{a\left(a-4\right)}$$

Short Solution Steps

Multiply \frac{a+2}{2a-8} times \frac{96}{a^{2}+2a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3a^{2}}{a-4}-\frac{\left(a+2\right)\times 96}{\left(2a-8\right)\left(a^{2}+2a\right)}$$

Factor the expressions that are not already factored in \frac{\left(a+2\right)\times 96}{\left(2a-8\right)\left(a^{2}+2a\right)}.

$$\frac{3a^{2}}{a-4}-\frac{96\left(a+2\right)}{2a\left(a-4\right)\left(a+2\right)}$$

Cancel out 2\left(a+2\right) in both numerator and denominator.

$$\frac{3a^{2}}{a-4}-\frac{48}{a\left(a-4\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a-4 and a\left(a-4\right) is a\left(a-4\right). Multiply \frac{3a^{2}}{a-4} times \frac{a}{a}.

$$\frac{3a^{2}a}{a\left(a-4\right)}-\frac{48}{a\left(a-4\right)}$$

Since \frac{3a^{2}a}{a\left(a-4\right)} and \frac{48}{a\left(a-4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3a^{2}a-48}{a\left(a-4\right)}$$

Do the multiplications in 3a^{2}a-48.

$$\frac{3a^{3}-48}{a\left(a-4\right)}$$

Expand a\left(a-4\right).

$$\frac{3a^{3}-48}{a^{2}-4a}$$

Expand

$$\frac{3\left(a^{3}-16\right)}{a\left(a-4\right)}$$

Short Solution Steps

Multiply \frac{a+2}{2a-8} times \frac{96}{a^{2}+2a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3a^{2}}{a-4}-\frac{\left(a+2\right)\times 96}{\left(2a-8\right)\left(a^{2}+2a\right)}$$

Factor the expressions that are not already factored in \frac{\left(a+2\right)\times 96}{\left(2a-8\right)\left(a^{2}+2a\right)}.

$$\frac{3a^{2}}{a-4}-\frac{96\left(a+2\right)}{2a\left(a-4\right)\left(a+2\right)}$$

Cancel out 2\left(a+2\right) in both numerator and denominator.

$$\frac{3a^{2}}{a-4}-\frac{48}{a\left(a-4\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a-4 and a\left(a-4\right) is a\left(a-4\right). Multiply \frac{3a^{2}}{a-4} times \frac{a}{a}.

$$\frac{3a^{2}a}{a\left(a-4\right)}-\frac{48}{a\left(a-4\right)}$$

Since \frac{3a^{2}a}{a\left(a-4\right)} and \frac{48}{a\left(a-4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3a^{2}a-48}{a\left(a-4\right)}$$

Do the multiplications in 3a^{2}a-48.

$$\frac{3a^{3}-48}{a\left(a-4\right)}$$

Expand a\left(a-4\right).

$$\frac{3a^{3}-48}{a^{2}-4a}$$